A087977 a(n) is the first term in the first chain of at least n consecutive numbers each having exactly four distinct prime factors.

210, 7314, 37960, 134043, 357642, 1217250, 1217250, 14273478, 44939642, 76067298, 163459742, 547163235, 2081479430, 2771263512, 11715712410, 17911205580, 56608713884, 118968284928, 118968284928, 585927201062

Offset

1,1

Comments

Eggleton and MacDougall show that there are no more than 419 terms in this sequence. - T. D. Noe, Oct 13 2008

a(24) > 10^13. - Donovan Johnson, Jan 15 2009

Links

Donovan Johnson, Table of n, a(n) for n = 1..23

Roger B. Eggleton and James A. MacDougall, Consecutive integers with equally many principal divisors, Math. Mag. 81 (2008), 235-248.

Example

a(6) = a(7) = 1217250 because the relevant 7 successive numbers have 4 distinct prime factors:
  1217250 = 2   *  3^2 *   5^3 * 541;
  1217251 = 7   * 17   *  53   * 193;
  1217252 = 2^2 * 23   * 101   * 131;
  1217253 = 3   * 47   *  89   *  97;
  1217254 = 2   * 19   * 103   * 311;
  1217255 = 5   * 13   *  61   * 307;
  1217256 = 2^3 *  3   *  67   * 757.

Mathematica

k=1; Do[While[Union[Table[Length[FactorInteger[i]], {i, k, k+n-1}]]!={4}, k++ ]; Print[k], {n, 1, 8}]
Module[{d4=Table[If[PrimeNu[n]==4, 1, 0], {n, 143*10^5}]}, Flatten[Table[ SequencePosition[d4, PadRight[{}, n, 1], 1], {n, 8}], 1][[All, 1]]] (* Requires Mathematica version 10 or later *) (* This generates the first 8 terms of the sequence *) (* Harvey P. Dale, Aug 25 2017 *)

Crossrefs

Cf. A080569 (m=3), A064708 (m=2).

Cf. A087978, A138206, A138207, A154573.

Sequence in context: A103604 A257711 A061133 * A185042 A323963 A023905

Adjacent sequences: A087974 A087975 A087976 * A087978 A087979 A087980

Keyword

nonn,fini

Author

Labos Elemer, Sep 26 2003

Extensions

More terms from Don Reble, Sep 29 2003

a(13)-a(19) from Donovan Johnson, Mar 06 2008

a(20)-a(23) from Donovan Johnson, Jan 15 2009

Status

approved